The logarithm operator is the inverse operation of exponential. The subscript number is the base of the logarithm and the expression is what is being operated on. The relationship with exponets can be expressed using the two equations below:
By restricting the logarithm operator to base illustrates the pattern that the operator captures.
Name  Property 

Product  
Quotient 
The exponential operator is closely related to the logarithm and radical operators. For example, given the scenario of exponential population growth, the relationship between the three operators is expressed below. Note, in this hypothetical scenario the initial population is represented with the value of .
Equation  Operator 

Exponent Given the growth rate and the time elapsed, the exponent operator returns the population. 

Logarithm Given the growth rate and the population the logarithm operator returns the time elapsed. 

Radical Given the time elapsed and the population the radical operator returns the growth rate. 
The exponentiation operator is a binary operator. The base is an expression or number that is being raised to some exponent. The exponent expression is denoted using superscript text.
Taking the logarithm of an number is the inverse operation of exponentiation. The subscript number is the base of the logarithm and the expression is the operand.
The radical operator returns the nth root of the provided expression. The radical operator is an alternative way of writing a fractional exponent.